JP 10-217 050 A discloses a laser processing machine for processing workpieces, in particular metal sheets, by piercing a workpiece to be processed by means of a laser beam, having a workpiece support for supporting a workpiece, a laser processing head and a beam receiver with a receiving opening for the laser beam, and an adjusting device. The laser processing head is arranged on the one side of the workpiece and the workpiece support and the beam receiver are arranged on the opposite side of the workpiece, and the laser beam enters the receiving opening of the beam receiver after piercing through the workpiece. In addition, in particular fumes and slag that occur at the machining point of the laser beam are extracted via the beam receiver. Finally, a beam receiver of the described kind can also be used to discharge sheet cut-outs produced by means of the laser beam from the processing area region of the laser processing machine. A workpiece support, having a brush area for supporting the workpiece, is provided with a recess for the beam receiver. The brush area extends right to the edge of the recess for the beam receiver. When processing flat metal sheets, the beam receiver assumes an upper end position along the beam axis of the laser beam, and projects right through the recess on the workpiece support. At its top face, the beam receiver located in the upper end position lies flush with the free end of the bristles of the brush area of the workpiece support. Accordingly, the sheets to be machined rest both on the brush area of the workpiece support and also on the top face of the beam receiver. To perform the desired processing, for example, to produce cut-outs, the sheet is moved perpendicularly to the laser beam over the brush area and the beam receiver. If a sheet to be processed is provided with a formation that protrudes downwardly with respect to the main plane of the sheet, then when the sheet is moved over the workpiece support this formation would collide with the beam receiver moved into the upper end position. To avoid such collisions, the beam receiver of the known laser processing machine is lowered by means of an adjusting device into a lower end position as soon as a formation protruding from the underside of the metal sheet approaches the beam receiver located in the upper end position. The lowering movement of the beam receiver is initiated with the aid of detectors, which are provided on the workpiece support close to the recess for the beam receiver and which, when the sheet moves over the workpiece support, are approached by the downwardly protruding formations of the metal sheet to be processed. In the lower end position, the beam receiver lies beneath the workpiece support, so that formations protruding from the underside of the metal sheet can be moved over the beam receiver without collisions. For cutting operations, with the described upper end position the known laser processing machine is provided merely with one single position of the beam receiver.